807 research outputs found
On the triviality of certain non-Riemannian models of gravitation
We prove in the Tucker-Wang approach to non-Riemannian Gravity that a general
homogeneous Lagrangian density in the general connection with order of
homogeneity of at least two, gives no contribution to the generalised Einstein
equations. Using this result other important cases are also considered.Comment: 12 pages, Latex, final version for Physics Letters
The Einstein static universe with torsion and the sign problem of the cosmological constant
In the field equations of Einstein-Cartan theory with cosmological constant a
static spherically symmetric perfect fluid with spin density satisfying the
Weyssenhoff restriction is considered. This serves as a rough model of space
filled with (fermionic) dark matter. From this the Einstein static universe
with constant torsion is constructed, generalising the Einstein Cosmos to
Einstein-Cartan theory.
The interplay between torsion and the cosmological constant is discussed. A
possible way out of the cosmological constant's sign problem is suggested.Comment: 8 pages, LaTeX; minor layout changes, typos corrected, one new
equation, new reference [5], completed reference [13], two references adde
An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges
The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses
{\it nonmetricity} and {\it torsion} as post-Riemannian structures. The sources
of MAG are the conserved currents of energy-momentum and dilation, shear and
spin. We present an exact static spherically symmetric vacuum solution of the
theory describing the exterior of a lump of matter carrying mass and dilation,
shear and spin charges.Comment: 13 pages, RevTe
Measurement Theory and General Relativity
The theory of measurement is employed to elucidate the physical basis of
general relativity. For measurements involving phenomena with intrinsic length
or time scales, such scales must in general be negligible compared to the
(translational and rotational) scales characteristic of the motion of the
observer. Thus general relativity is a consistent theory of coincidences so
long as these involve classical point particles and electromagnetic rays
(geometric optics). Wave optics is discussed and the limitations of the
standard theory in this regime are pointed out. A nonlocal theory of
accelerated observers is briefly described that is consistent with observation
and excludes the possibility of existence of a fundamental scalar field in
nature.Comment: LaTeX springer style lamu.cls, 2 figures, 16 pages, published in:
Black Holes: Theory and Observation: Proceedings of the 179th W.E. Heraeus
Seminar, held August 1997 in Bad Honnef, Germany. F.W. Hehl et al.(eds).
(Springer, Berlin Heidelberg 1998
Metric-affine gauge theory of gravity II. Exact solutions
In continuing our series on metric-affine gravity (see Gronwald IJMP D6
(1997) 263 for Part I), we review the exact solutions in this theory.Comment: Revtex file, 25 pages, final version to appear in IJMP
Test Matter in a Spacetime with Nonmetricity
Examples in which spacetime might become non-Riemannian appear above Planck
energies in string theory or, in the very early universe, in the inflationary
model. The simplest such geometry is metric-affine geometry, in which {\it
nonmetricity} appears as a field strength, side by side with curvature and
torsion. In matter, the shear and dilation currents couple to nonmetricity, and
they are its sources. After reviewing the equations of motion and the Noether
identities, we study two recent vacuum solutions of the metric-affine gauge
theory of gravity. We then use the values of the nonmetricity in these
solutions to study the motion of the appropriate test-matter. As a
Regge-trajectory like hadronic excitation band, the test matter is endowed with
shear degrees of freedom and described by a world spinor.Comment: 14 pages, file in late
PP-waves with torsion and metric-affine gravity
A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a
nonvanishing parallel spinor field; here the connection is assumed to be
Levi-Civita. We generalise this definition to metric compatible spacetimes with
torsion and describe basic properties of such spacetimes. We use our
generalised pp-waves for constructing new explicit vacuum solutions of
quadratic metric-affine gravity.Comment: 17 pages, LaTeX2
Axial Torsion-Dirac spin Effect in Rotating Frame with Relativistic Factor
In the framework of spacetime with torsion and without curvature, the Dirac
particle spin precession in the rotational system is studied. We write out the
equivalent tetrad of rotating frame, in the polar coordinate system, through
considering the relativistic factor, and the resultant equivalent metric is a
flat Minkowski one. The obtained rotation-spin coupling formula can be applied
to the high speed rotating case, which is consistent with the expectation.Comment: 6 page
Strings in gravity with torsion
A theory of gravitation in 4D is presented with strings used in the material
action in spacetime. It is shown that the string naturally gives rise to
torsion. It is also shown that the equation of motion a string follows from the
Bianchi identity, gives the identical result as the Noether conservation laws,
and follows a geodesic only in the lowest order approximation. In addition, the
conservation laws show that strings naturally have spin, which arises not from
their motion but from their one dimensional structure.Comment: 16 page
An assessment of Evans' unified field theory I
Evans developed a classical unified field theory of gravitation and
electromagnetism on the background of a spacetime obeying a Riemann-Cartan
geometry. This geometry can be characterized by an orthonormal coframe theta
and a (metric compatible) Lorentz connection Gamma. These two potentials yield
the field strengths torsion T and curvature R. Evans tried to infuse
electromagnetic properties into this geometrical framework by putting the
coframe theta to be proportional to four extended electromagnetic potentials A;
these are assumed to encompass the conventional Maxwellian potential in a
suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity
was adopted by Evans to describe the gravitational sector of his theory.
Including also the results of an accompanying paper by Obukhov and the author,
we show that Evans' ansatz for electromagnetism is untenable beyond repair both
from a geometrical as well as from a physical point of view. As a consequence,
his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and
typos removed, partly reformulated, taken care of M.W.Evans' rebutta
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